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Numbers in group theory
This page contains numbers appearing in . List of numbers in group theory *The has 101 es. *The constant term in the T2A is equal to 104. *The largest of any element in the Monster group is 119. There is also no other with elements of larger order. *The Frobenius kernel of the smallest non-solvable is the of order 121. **It is also the fourth largest undulating square number; this has been proved by David Moews. **According to the , the numbers 121 and 125 are the seventh largest s not separated by a . **Its prime factorization is 112. **121 is the second Friedman number. *The has 133. *The McKay-Thompson series of span a 163- . *The exceptional Lie algebra has dimension 190. **It is also the 19th , and therefore the number of tiles in a double-18 set. *There are 194 es in the Monster group. *The exceptional Lie algebra has dimension 248. **It is also the number of in . **Furthermore, it was the number of during 1965–1990. *'720' is equal to 6!, the factorial of 6. Consequently, it is the order of the of degree 6, which is isomorphic to , and has an . *The constant term in the of the is equal to 744. *'1,440' is the order of the of the . **It is also the number of s in a . Consequently, it is also mentioned in 's famous book in chapter 14, where the planet on which the lamplighter lives has 1,440 sunsets in the course of one Earth day. *There are 4,060 points in the smallest faithful permutation representation of the ; its one-point stabilizer is the automorphism group of the . **It is also the number of known nonnegative integers which cannot be written as a ; the largest of which is 1,290,740. *The smallest faithful linear representation of the Baby monster group over any field has dimension 4,370. *The smallest faithful linear representation of the Baby monster group over the complex numbers has dimension 4,371. *The coefficient of the linear term in the T2A is equal to 4,372. *There are 196,560 points in the smallest faithful permutation representation of the ; its one-point stabilizer is the . *The smallest faithful linear representation of the Monster group over any field has dimension 196,882. *The smallest faithful linear representation of the Monster group over the complex numbers has dimension 196,883. *The has dimension 196,884. **It is also the coefficient of the linear term in the of the . *There are (5)='9,999,360' 5 × 5 over , therefore it is the order of a matrix group . *'16,776,960' is the order of the simple group , which is isomorphic to PGL(2,256) and SL(2,256). It is one of the few over a finite field of characteristic 2, for which the Sylow 2-subgroup is not the largest Sylow subgroup. *The order of a simple group is almost never a . The emphasis is on "almost", since for s, the order of the simple group is a square number. The simple group has order '''138,297,600', which is the smallest perfect power that is also an order of a simple group. *'4,585,351,680' is the second smallest order with more than one simple group. *The order of a simple group is almost never an . The emphasis is on "almost", since there is a simple group of order 16,938,986,400, which is an Achilles number. *'281,474,976,645,120' is the order of the simple group , which is isomorphic to PGL(2,65536) and SL(2,65536). It is one of the few over a finite field of characteristic 2, for which the Sylow 2-subgroup is not the largest Sylow subgroup. Orders of non-abelian simple groups This list contains with unusual properties, such as: # Its order has at most four distinct prime factors, or is a ; # the p''-Sylow group (where ''p = 2 for alternating groups) is not the largest Sylow subgroup; and/or # there is an exceptional isomorphism, outer automorphism group, or Schur multiplier. Sporadic groups have their own section. Sporadic group-related numbers Approximations of these numbers For 20,160: For 25,920: {{Approximations|sci = \(2.5920*10^4\) (exact)|fast = \(f_2(11) Category:Numbers Category:Numbers in group theory Category:Lists Category:Class 1 Category:Class 2 Category:Numbers with 3 digits Category:Unnamed numbers with 4 to 6 digits Category:Unnamed numbers with 7 to 29 digits